How Forces Affect Motion

Chapter at a glance

• Force is a vector quantity that requires both magnitude and direction; its SI unit is the newton (N).
• Balanced forces are equal in magnitude and opposite in direction; they produce zero net force and no change in motion.
• Unbalanced forces produce a non-zero net force; the magnitude of net force is the difference (opposite directions) or sum (same direction) of the individual forces.
• The force of friction always acts opposite to the direction of motion (or attempted motion) and depends on the nature of the surfaces in contact.
• Newton’s first law states that an object at rest remains at rest and an object in uniform motion continues in the same state unless a net force acts on it.
• Newton’s second law states that the acceleration produced by a net force is proportional to the force and inversely proportional to the mass of the object (F = ma).
• Newton’s third law states that forces always occur in equal-and-opposite pairs acting on two different objects.
• The gravitational force on an object near the Earth’s surface is F = mg, where g ≈ 9.8 m s⁻².

Definitions and laws

• Newton’s first law of motion: “An object at rest remains at rest, and an object in motion continues to move with a constant velocity, unless a net force acts upon the object.”
• Newton’s second law of motion: “When a net force acts on an object, the object accelerates in the direction of the net force. The magnitude of the acceleration is proportional to the magnitude of the net force and is inversely proportional to the mass of the object.”
• Mathematically: F = ma (direction of a same as direction of net F).
• One newton is defined as the force that produces an acceleration of 1 m s⁻² on an object of mass 1 kg.
• Newton’s third law of motion: “Whenever one object is exerting a force on a second object, the second object is simultaneously exerting an equal and opposite force on the first object.” (The two forces act on different objects.)
• Gravitational force on an object: F = mg, where g = 9.8 m s⁻² (nearly constant near the Earth’s surface).

Important diagrams and activities

• Fig. 6.1 (kicking/striking a ball, squeezing a lemon) — shows that a force can change the state of rest, speed, direction or shape of an object.
• Fig. 6.2 (spring balance measuring weight) — illustrates measurement of the magnitude of a force.
• Fig. 6.3a,b and Fig. 6.4 (pushing a box, floating ball, tug-of-war) — demonstrate balanced vs unbalanced forces.
• Fig. 6.5 and Fig. 6.6 (two forces in same or opposite directions) — show calculation of net force magnitude and direction.
• Activity 6.1 (stack of coins released by stretched rubber band on different surfaces) — shows that friction depends on the nature of surfaces and opposes motion.
• Activity 6.2 (spring balance pulling a wooden block on different surfaces) — gives a direct measure of the force of friction.
• Fig. 6.11 (applied force, friction, weight and normal force on a block) — shows all forces acting on a pushed object.
• Fig. 6.18–6.20 and Fig. 6.22–6.30 (catching a ball, airbag, rocket launch, walking, canoe, balloon) — illustrate Newton’s third law and action-reaction pairs.
• Fig. 6.34–6.35 (two boxes connected by string) — shows treatment of a system of objects and external vs internal forces.

Common misconceptions and exam pitfalls

• “A force is needed to keep an object moving at constant velocity” — the chapter explicitly corrects this; zero net force means constant velocity (including non-zero velocity).
• Action-reaction forces cancel each other — they act on different objects, so they never cancel for the motion of either object.
• Heavier objects always accelerate more under the same force — acceleration is inversely proportional to mass (F = ma).
• Net force = 0 implies the object is at rest — uniform motion is also possible.
• Students forget to specify direction of net force or acceleration when applying Newton’s laws.

Formula sheet